CN103364418A - Grating shearing two-dimensional imaging system and method - Google Patents

Abstract

The invention provides a grating shearing two-dimensional imaging system and method. The imaging system comprises a light source device, a beam splitting grating, a sample table, an analysis grating and a detector, wherein the light source device is used for generating a plurality of slit sources, and each slit source generates an X ray light beam irradiating the beam splitting grating; the beam splitting grating is used for cutting a light beam into a one-dimensional light beam array; the sample table is used for bearing a sample; the analysis grating is used for generating different light intensity backgrounds to reinforce or inhibit a refraction or scattering signal of the sample; the detector is used for detecting the change of backgrounds and space positions of light intensity and collecting projection images of the sample under different light intensity backgrounds. The grating shearing two-dimensional imaging device and method can be used for quickly collecting images and are high in density resolution, high in density non-uniformity resolution and capable of meeting application demands of medical detection, safety inspection, industrial detection and the like; the sample can be arranged in front of and behind the beam splitter grating, and thus the radiation dosage of the sample is low.

Description

Grating shearing two-dimensional imaging system and grating shearing two-dimensional imaging method

Technical field

The present invention relates to technical field of imaging, particularly relate to a kind of grating shearing two-dimensional imaging system and grating shearing two-dimensional imaging method.

Background technology

The roentgen has found X ray in 1895, and wins first Nobel Prize in physics on Dec 10th, 1901.The X-ray photographs of wide-spread roentgen madam's hand has disclosed X ray and has had powerful penetration power, shows that the X ray direct imaging just can see the inner structure of sample.This based on material to the image-forming mechanism of X ray absorption difference last century the fifties be widely used in the human medical imaging, and in last century the eighties begin for the human body three-dimensional imaging.Although this imaging technique based on the X ray mechanism of absorption when observing heavy element formation article, can obtain the sufficiently high image of contrast (being contrast), when observing light element formation article, the image that only can obtain to blur.Its main cause is that the contained electron number of light element atom is few, and it is not little that light element consists of the article density difference, and mobility scale is between 1%-5%, and a little less than not only X ray being absorbed, and it is little that X ray is absorbed difference, can not form sufficiently high contrast.Thereby based on the image-forming mechanism of traditional attenuation by absorption when checking skeleton, can obtain the sufficiently high image of contrast, yet when checking the tumour that is consisted of by light element, can not obtain the sufficiently high image of contrast.

X-ray phase contrast imaging research starts from the nineties in last century, and more than two decades has been arranged up till now.X-ray phase contrast imaging is aspect detection light element constitute, and it is much higher that its detection sensitivity absorbs imaging than X ray, has vast potential for future development aspect medical imaging.Developed four kinds of X-ray phase contrast imaging methods, the grating shearing formation method that wherein utilizes grating to extract the sample phase information has the possibility of practical application most, its maximum advantage be can with the combination of conventional X ray light source.In X ray grating shearing imaging research, the researchist has also found the scattering image-forming mechanism, it is to be formed by the multiple refraction of a lot of molecules in the sample to X ray, and this image-forming mechanism is relatively more responsive to the structures such as micropore, microvesicle, particulate, crystallite and powder in the sample.

Utilizing at present raster scanning extraction phase information and scattered information is the main flow that develops in the world, yet the method for raster scanning does not meet the simple and rapid requirement of medical imaging.

Summary of the invention

An object of the present invention is to provide a kind of grating shearing two-dimensional imaging system, to realize easy fast imaging, satisfy the application demand of the aspects such as medical science detection, safety inspection, industrial detection.

Another object of the present invention provides and a kind ofly can realize easy fast imaging, satisfies the grating shearing two-dimensional imaging method of the aspect application demands such as medical science detection, safety inspection, industrial detection.

Grating shearing two-dimensional imaging of the present invention system comprises:

Light supply apparatus, for generation of many seam light sources, every seam light source all produces the X ray light beam of illumination beam splitter grating;

Beam-splitting optical grating is used for described light beam is divided into the one dimension beam array;

Sample stage is used for the carrying sample;

Analyze grating, for generation of different light intensity backgrounds, refraction signal or the scattered signal of enhancer or inhibitor sample;

Detector is used for surveying the background of light intensity and the variation of locus, gathers the projection image of described sample under the different light intensity background.

Grating shearing two-dimensional imaging method of the present invention comprises:

Adjust light supply apparatus, the light beam irradiates beam-splitting optical grating that described light supply apparatus is produced;

Adjust beam-splitting optical grating, make the beam-splitting optical grating plane perpendicular to the described beam center direction of propagation, and be the One Dimension Periodic beam array with described light beam beam splitting;

Adjust and analyze grating, the one dimension beam array that the described beam-splitting optical grating of described analysis grating alignment is produced;

Measure displacement curve, when n.s., survey the variation of background light intensity by detector, in the plane of the direction of propagation, normal beam center, move described light source grating or grizzly bar target or beam-splitting optical grating or analyze grating along the direction perpendicular to grizzly bar, adjust the shear displacemant between the one dimension beam array of analyzing grating and beam-splitting optical grating generation, detector records the displacement curve that background light intensity shear displacemant changes;

The projection image of detector collected specimens, shear displacemant between the one dimension beam array of analyzing the generation of grating and described beam-splitting optical grating is adjusted at the collection position that the light intensity background satisfies imaging requirements, put into sample, gather described sample in the projection image of described light intensity background by described detector.

Grating shearing two-dimensional imaging system of the present invention and grating shearing two-dimensional imaging method have following advantage:

(1) grating shearing two-dimensional imaging system and method for the present invention only need be taken a width of cloth picture, just can realize two-dimentional sxemiquantitative imaging; Only need to take the different picture of three width of cloth light intensity backgrounds, just can realize the two-dimensional quantitative imaging; With imaging system at present in vogue and method compare both at home and abroad, not only density resolution is high, Density inhomogeneity resolution is high, and method is easy, the width of cloth number of required shooting picture is few, the required radiation dose of sample is low, can the Quick Acquisition image, satisfy the application demand of the aspects such as medical science detection, safety inspection, industrial detection; (2) the sxemiquantitative imaging only need be taken a width of cloth picture, quantitative imaging only need be taken the different picture of three width of cloth light intensity backgrounds, therefore, the grating shearing two-dimensional imaging method that the present invention proposes is for the phase contrast dynamic imaging in future, the parallel fast imaging of multiple image-forming mechanism lay the foundation.

Description of drawings

Fig. 1 (a), Fig. 1 (b) are the structural representation of grating shearing imaging device of the present invention, in the grating shearing imaging device in Fig. 1 (a), the grating grizzly bar is parallel to sample rotating shaft (being Y-axis), when along X-direction mobile light source grating or grizzly bar target or beam-splitting optical grating or analysis grating, the capital causes that the one dimension beam array that beam-splitting optical grating produces analyzes grating generation shear displacemant relatively, and each pixel of detector can measure the displacement curve that background light intensity shear displacemant changes; In the grating shearing imaging device in Fig. 1 (b), the grating grizzly bar is perpendicular to sample rotating shaft (being Y-axis), when along Y direction mobile light source grating or grizzly bar target or beam-splitting optical grating or analysis grating, the capital causes that the one dimension beam array that beam-splitting optical grating produces analyzes grating generation shear displacemant relatively, and each pixel of detector can measure the displacement curve that background light intensity shear displacemant changes;

Fig. 2 is that sample of the present invention is to the schematic diagram of X ray beam absorption attenuation, wherein I ₀Be incident intensity, I is output intensity;

Fig. 3 is sample of the present invention produces refraction action to the X ray light beam schematic diagram;

Fig. 4 is sample of the present invention produces scattering process to the X ray light beam schematic diagram;

Fig. 5 (a) and the displacement curve of Fig. 5 (b) for the one dimension beam array shear displacemant variation of the relative beam-splitting optical grating generation of light intensity analysis grating, Fig. 5 (a) analyzes the one dimension beam array (striped filling) of the relative beam-splitting optical grating generation of grating (four black) along the displacement curve of X-axis shear displacemant variation for light intensity, and shear displacemant is separately fixed at details in a play not acted out on stage, but told through dialogues position, left half bright field position, bright field position, right half bright field position, details in a play not acted out on stage, but told through dialogues position between (from left to right) analysis grating (four black) and the beam-splitting optical grating one dimension beam array (striped filling); Fig. 5 (b) analyzes the one dimension beam array (striped filling) of the relative beam-splitting optical grating generation of grating (four black) along the displacement curve of Y-axis shear displacemant variation for light intensity, and shear displacemant is separately fixed at details in a play not acted out on stage, but told through dialogues position, second bright field position, bright field position, first bright field position, details in a play not acted out on stage, but told through dialogues position between (from top to bottom) analysis grating (four black) and the beam-splitting optical grating one dimension beam array (striped filling);

Mark is illustrated as among the figure: the 1-light beam; The 2-beam-splitting optical grating; The 3-sample stage; 4-analyzes grating; The 5-detector.

Embodiment

For the purpose, technical scheme and the advantage that make the embodiment of the invention clearer, below in conjunction with the accompanying drawing in the embodiment of the invention, technical scheme in the embodiment of the invention is clearly and completely described, obviously, described embodiment is the present invention's part embodiment, rather than whole embodiment.The element of describing in an accompanying drawing of the present invention or a kind of embodiment and feature can combine with element and the feature shown in one or more other accompanying drawing or the embodiment.Should be noted that for purpose clearly, omitted expression and the description of parts that have nothing to do with the present invention, known to persons of ordinary skill in the art and processing in accompanying drawing and the explanation.Based on the embodiment among the present invention, those of ordinary skills belong to the scope of protection of the invention not paying the every other embodiment that obtains under the creative work prerequisite.

Referring to Fig. 1 (a), Fig. 1 (b), grating shearing imaging system of the present invention comprises:

Light supply apparatus, for generation of many seam light sources, every seam light source all produces the X ray light beam of illumination beam splitter grating;

Beam-splitting optical grating 2, being used for described light beam beam splitting is the One Dimension Periodic beam array;

Sample stage 3 is used for the carrying sample;

Analyze grating 4, for generation of different light intensity backgrounds, refraction signal or the scattered signal of enhancer or inhibitor sample;

Detector 5 is used for surveying the background of light intensity and the variation of locus, gathers the projection image of described sample under the different light intensity background.

A width of cloth picture only need be taken by above-mentioned grating shearing two-dimensional imaging system, just can realize two-dimentional sxemiquantitative imaging; Only need to take the different picture of three width of cloth light intensity backgrounds, just can realize the two-dimensional quantitative imaging; Compare with the method that prevails at present both at home and abroad, not only density resolution is high, Density inhomogeneity resolution is high, and method is easy, the width of cloth number of required shooting picture is few, the required radiation dose of sample is low, can the Quick Acquisition image, satisfy the application demand of the aspects such as medical science detection, safety inspection, industrial detection.The sxemiquantitative imaging only need be taken a width of cloth picture, quantitative imaging only need be taken the different picture of three width of cloth light intensity backgrounds, therefore, the grating shearing two-dimensional imaging method that the present invention proposes is for the phase contrast dynamic imaging in future, the parallel fast imaging of multiple image-forming mechanism lay the foundation.

Optionally, described light supply apparatus comprises pointolite or seam light source; Or described light supply apparatus comprises expansion light source and light source grating; Or described light supply apparatus is the grizzly bar target with light source grating complementary structure; Described light source grating is used for that described expansion light source is divided into one dimension and stitches light source more, or described grizzly bar target directly produces one dimension and stitches light source more.

Described grizzly bar target is the structure of setting that target light source and light source grating are become one.

Optionally, described sample stage is arranged between beam-splitting optical grating and the light supply apparatus and the setting of next-door neighbour's beam-splitting optical grating; Or described sample stage is arranged at beam-splitting optical grating and analyzes between the grating and the setting of next-door neighbour's beam-splitting optical grating.

Optionally, described light supply apparatus is that every seam light source all produces the light supply apparatus of the X ray light beam of illumination beam splitter grating for generation of many seam light sources; And/or,

Described light source grating, described beam-splitting optical grating and described analysis grating are absorption grating or described beam-splitting optical grating is phase grating, and described light source grating and described analysis grating are absorption grating; And/or described light source grating is pressed close to described light source and is placed; And/or,

The grizzly bar of described light source grating be wider than or equal to stitch wide, or the grizzly bar of described grizzly bar target be less than or equal to the seam wide;

The period-producer pin-hole imaging relation of the cycle of described light source grating or described grizzly bar target and described analysis grating, pin hole is any seam on the beam-splitting optical grating; And/or,

Described beam-splitting optical grating and the distance of analyzing between the grating are 0.1～5 meter; And/or,

The cycle of described beam-splitting optical grating is 1～100 micron; And/or,

The grizzly bar of described beam-splitting optical grating is wide and seam is wide equates; And/or,

The cycle of described analysis grating equals 1/2nd of the geometric projection in described beam-splitting optical grating cycle or geometric projection; And/or,

The grizzly bar of described analysis grating is wide and seam is wide equates; And/or,

Described detector is pressed close to described analysis grating and is placed; And/or,

Described detector comprises one dimensional linear array or the two-dimensional array that a plurality of probe units consist of.

Optionally, when described light source grating or beam-splitting optical grating or described analysis grating were absorption grating, its grizzly bar thickness was for making at least through light intensity attenuation to 10% of incident intensity required thickness; When described beam-splitting optical grating was phase grating, its grizzly bar thickness needed to make the phase shift that obtains π or pi/2 through light beam.

The following describes the flow process of the grating shearing two-dimensional imaging method that the embodiment of the invention provides, the method comprises the steps:

(a) adjust light supply apparatus, the X ray light beam irradiates beam-splitting optical grating that described light supply apparatus is produced;

(b) adjust beam-splitting optical grating, make the beam-splitting optical grating plane perpendicular to the described beam center direction of propagation, and be the One Dimension Periodic beam array with described light beam beam splitting;

(c) adjust the analysis grating, the one dimension beam array that the described beam-splitting optical grating of described analysis grating alignment is produced;

(d) measure displacement curve, surveying the background light intensity by detector changes, in the plane of the direction of propagation, normal beam center, move described light source grating or grizzly bar target or beam-splitting optical grating or analyze grating along the direction perpendicular to grizzly bar, adjust the shear displacemant between the one dimension beam array of analyzing grating and beam-splitting optical grating generation, detector records the displacement curve that background light intensity shear displacemant changes;

(e) projection image of detector collected specimens, shear displacemant between the one dimension beam array of analyzing the generation of grating and described beam-splitting optical grating is adjusted at the collection position that the background light intensity satisfies imaging requirements, put into sample, gather the projection image of described sample under described light intensity background by described detector.

Above-mentioned grating shearing two-dimensional imaging method only need be taken a width of cloth picture, just can realize two-dimentional sxemiquantitative imaging; Only need to take the different picture of three width of cloth light intensity backgrounds, just can realize the two-dimensional quantitative imaging; Compare with the imaging system that prevails at present both at home and abroad and method, not only density resolution is high, Density inhomogeneity resolution is high, and method is easy, the width of cloth number of required shooting picture is few, the required radiation dose of sample is low, can the Quick Acquisition image, satisfy the application demand of the aspects such as medical science detection, safety inspection, industrial detection.The sxemiquantitative imaging only need be taken a width of cloth picture, quantitative imaging only need be taken the different picture of three width of cloth light intensity backgrounds, therefore, the grating shearing two-dimensional imaging method that the present invention proposes is for the phase contrast dynamic imaging in future, the parallel fast imaging of multiple image-forming mechanism lay the foundation.

Optionally, described light supply apparatus comprises expansion light source and light source grating, described " adjusting light supply apparatus; the light beam irradiates beam-splitting optical grating that described light supply apparatus is produced " is specially " adjust light source and light source grating; make described light source grating that described light source is divided into one dimension and stitch light source more; or adjust described grizzly bar target and produce one dimension and stitch light source more, make every seam light source can both produce the light beam irradiates beam-splitting optical grating ".

Optionally, described light intensity background comprises: bright field background, details in a play not acted out on stage, but told through dialogues background and/or half bright field background; Described half bright field background comprises right half bright field background and/or left half bright field background, perhaps comprises first bright field background and/or second bright field background;

Described acquired projections looks like to comprise: gather described sample at the light field image under the described bright field background, at the dark field image under the described details in a play not acted out on stage, but told through dialogues background and/or half light field image under described half bright field background; Described half light field image comprises: left half light field image and/or right half light field image perhaps comprise first light field image and/or second light field image.

Optionally, after the projection image of detector collected specimens, also comprise step (f): from the projection image of described collection, extract the sxemiquantitative of described sample or the step of quantitative description information.

Optionally, sxemiquantitative or the quantitative description information of the described sample of extraction specifically comprise from the projection image of described collection:

(f1) set up the grating shearing imaging equation: with the displacement curve that the cosine function curve records, set up thing function mathematical model, according to the convolution algorithm of thing function and match displacement curve, set up the grating shearing imaging equation;

(f2) try to achieve the mathematic(al) representation of the projection image that detector gathers: the mathematic(al) representation of trying to achieve respectively described light field image, dark field image and half light field image according to described grating shearing imaging equation;

(f3) respectively the mathematic(al) representation of described light field image, dark field image and half light field image is out of shape, obtains the semi-quantitative expressed formula of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample;

Or

(f4) according to the quantitative relationship between the mathematic(al) representation of described light field image, dark field image and half light field image, obtain the quantitative expression of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample.

In the embodiment of the invention, the beam center direction of propagation is the Z direction, in the plane of the direction of propagation, normal beam center, is directions X perpendicular to the direction of sample rotating shaft, the direction that is parallel to the sample rotating shaft is Y-direction, grating grizzly bar or be parallel to the sample rotating shaft or perpendicular to the sample rotating shaft.

In the technique scheme, the light intensity background of described acquired projections picture can be: bright field background, details in a play not acted out on stage, but told through dialogues background and/or half bright field background; Described half bright field background can be: left half bright field background, right half bright field background and/or first bright field background, second bright field background; Described acquired projections looks like can be: half light field image of the light field image of the corresponding described bright field background of described sample, the dark field image of the corresponding described details in a play not acted out on stage, but told through dialogues background of described sample, the corresponding described half bright field background of described sample; Described half light field image comprises: left half light field image, right half light field image and/or first light field image, second light field image.

Described acquired projections looks like to be detector and directly gathers, and therefrom can extract sxemiquantitative or quantitative projection image, can be used for dynamic imaging or the Quantitative detection of detected article.

For example, the grating shearing formation method also can comprise sxemiquantitative formation method and/or quantitative imaging method.In the sxemiquantitative formation method that the present invention proposes, gather a width of cloth projection image, just can obtain or with attenuation by absorption with the refraction angle or with the scattering angle variance or with the obvious relevant sxemiquantitative image of delustring decay; In the quantitative imaging method, gather at the most three width of cloth images, just can therefrom extract the attenuation by absorption picture, refraction angle picture, scattering angle variance picture of sample or delustring decay and the quantitative image such as look like.

In the step (f1), the process of setting up the grating shearing imaging equation is:

The first step, the impulse response function that is described as the picture system performance is obtained in the filter action of the one dimension beam array that the described beam-splitting optical grating of the described analysis grating pair of mathematical description produces; Second step is set up sample to the mathematical model of X ray effect, writes out the mathematical expression of thing function; In the 3rd step, the convolution of calculating thing function and impulse response function is set up the grating shearing imaging equation.

The first step: the filter action of the one dimension beam array that the described beam-splitting optical grating of the described analysis grating pair of mathematical description produces.Because the one dimension beam array that beam-splitting optical grating produces and analysis grating all are the One Dimension Periodic functions, has the identical cycle, the shear displacemant of the one dimension beam array that the relative beam-splitting optical grating of analysis grating produces can be adjusted correlativity between the two, is computing cross-correlation so analyze the filter action of the one dimension beam array of grating pair beam-splitting optical grating generation at mathematics.

In the grating shearing imaging system that Fig. 1 (a) or Fig. 1 (b) describe, each grating grizzly bar is parallel with Y or X-axis, when along X or Y direction mobile light source grating or grizzly bar target or beam-splitting optical grating or analysis grating, will cause the one dimension beam array that beam-splitting optical grating produces and analyze between the grating shear displacemant occurs, each pixel of detector (or being called probe unit) can measure background light intensity shear displacemant and the displacement curve that changes, because the displacement curve that each pixel records is identical, satisfy translation invariance at imaging surface, so displacement curve is exactly the impulse response function of imaging system.The one dimension beam array that Fig. 5 (a) or Fig. 5 (b) produce for beam-splitting optical grating and analyze between the grating displacement curve when carrying out shear displacemant along X or Y direction; Because the similar cosine curve of displacement curve shape, in order to utilize the symmetric property of cosine curve, simplify the mathematical expression that extracts refraction and scattered information, so with cosine curve match displacement curve S (θ _g), its expression formula is:

$S\left({\mathrm{\θ}}_g\right)\≈\stackrel{\‾}{S}[1+V_0\cos \left(\frac{2\mathrm{\πD}}{p}{\mathrm{\θ}}_g\right)],---\left(1\right)$

Wherein

Or

For analyzing the relative beam-splitting optical grating of grating at the angle of shear displacement of X or Y direction, x _gOr y _gFor analyzing one dimension beam array that the relative beam-splitting optical grating of grating produces at the shear displacemant of X or Y direction, D is beam-splitting optical grating and analyzes the distance on direction of beam propagation between the grating, p also is the cycle of displacement curve for analyzing the cycle of grating on X or Y direction

Displacement curve mean value during for n.s., S _MaxAnd S _MinBe respectively maximal value and the minimum value of displacement curve,

The visibility of displacement curve during for n.s..The corresponding bright field of a point on the displacement curve among Fig. 5 (a), the corresponding details in a play not acted out on stage, but told through dialogues of d point, corresponding left half bright field of b point, corresponding right half bright field of c point.The corresponding bright field of a point on the displacement curve among Fig. 5 (b), the corresponding details in a play not acted out on stage, but told through dialogues of d point, corresponding second bright field of b point, corresponding first bright field of c point.Bright field represents the one dimension beam array of beam-splitting optical grating generation almost all by analyzing grating, details in a play not acted out on stage, but told through dialogues represent one dimension beam array that beam-splitting optical grating produces almost complete analyzed grating stop, half bright field represents in the one dimension beam array of beam-splitting optical grating generation, half analyzed grating stops, half is by analyzing grating.

Second step: set up thing function mathematical model.Before setting up thing function mathematical model, first to a bit defining in the sample.In two-dimensional imaging, a bit (x, y) is not a two-dimensional geometry point on the object plane of sample place, but the thing cell area Δ x Δ y centered by (x, y), the size of Δ x and Δ y is determined by dimension of light source and detector resolution.

Sample produces absorption, refraction and three kinds of effects of scattering to incident X-rays.Absorbing (comprising inelastic scattering) is an X ray energy is converted into heat energy in sample dissipation process, as shown in Figure 2, has described sample to incident X-rays attenuation by absorption action diagram picture.

According to Fig. 2, a bit (x, y) can be expressed as the absorption by this light in the sample:

The following formula left side represents incident beam, and irradiating light beam is expressed on the right, wherein

Expression beam angle vector,

$M(x,y)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{\μ}(x,y,z)\mathrm{dz},---\left(3\right)$

Wherein μ (x, y, z) is the linear absorption coefficient of sample.(2) physical significance of formula is, absorbs to cause the light intensity decay, but does not change radiation direction.(2) formula can also be expressed as weight expression:

Refraction is the process of an energy conservation, as shown in Figure 3, has described the image of sample to the incident X-rays refraction action.According to Fig. 3, a bit (x, y) can be expressed as the refraction by this light in the sample:

The following formula left side represents incident beam, and irradiating light beam is expressed on the right, wherein Expression beam angle vector,

Be the refraction angle vector, its mathematical expression is:

$\stackrel{\→}{\mathrm{\θ}}(x,y)=-\underset{-\∞}{\overset{\∞}{\∫}}\▿\mathrm{\δ}(x,y,z)\mathrm{dz}$

$=-\underset{-\∞}{\overset{\∞}{\∫}}(\frac{\∂\mathrm{\δ}(x,y,z)}{\∂x}{\stackrel{\→}{e}}_x+\frac{\∂\mathrm{\δ}(x,y,z)}{\∂y}{\stackrel{\→}{e}}_y)\mathrm{dz},---\left(6\right)$

$={\stackrel{\→}{e}}_x{\mathrm{\θ}}_x(x,y)+{\stackrel{\→}{e}}_y{\mathrm{\θ}}_y(x,y)$

Wherein δ (x, y, z) is sample refractive index real part attenuation rate.(5) physical significance of formula is, refraction changes radiation direction, but does not change light intensity.(5) formula can also be written as weight expression:

Scattering is caused by the inner a lot of short grained multiple refractions of cell area, also is the process of an energy conservation, as shown in Figure 4, has described the image of sample to the incident X-rays scattering process.The difference of scattering and refraction is, refraction is done as a whole research to cell area on the sample object plane, namely cell area on the sample object plane as a micro prisms, the inhomogeneous character of this cell area inside is then studied in scattering, and bubble, particle, micropore, crystallite and the impurity etc. that namely are equivalent to study micro prisms inside are inhomogeneous.Therefore, for each cell area, only have a refracted ray and a refraction angle, many scattered beams and a plurality of scattering angle are but arranged.In other words, scattering is the process that a light beam disperses.Because sample has certain thickness, in cell area inside along direction of beam propagation, it is random that each granule distributes, the refraction that former and later two granules produce is separate, the angle that the each refraction of granule makes incident ray depart from incident direction is random, so according to central limit theorem, scattering angle is to obey two-dimentional normal state statistical distribution centered by incident angle (perhaps refraction angle), can describe the scattering angular distribution scope with variance.According to Fig. 4, when a light was injected sample, because scattering causes dispersion, emergent ray was divided into two parts, scattered beam and scattered beam not, and scattered beam is still propagated along incident direction, and scattered beam departs from the incident direction propagation.Along with light is walked in sample, the continuous generation of scattering events, scattered beam constantly produces, and scattared energy strengthens gradually, and scattered beam does not slacken gradually, scattared energy does not weaken gradually, is called the delustring decay.Of particular note, every light all may run into the inner a plurality of short grained refractions of cell area, need to continue scattered beam and this scattered beam of being departed from for the first time by granule refraction generation for the first time to be considered respectively by the scattered beam that follow-up granule refraction generation further departs from, this is because scattared energy is once to depart from decision by what unirefringence produced, and repeatedly departing from that later repeatedly refraction produces only makes the scattared energy distribution range larger, increase the scattering angle variance, and work hardly to increasing or reduce scattared energy.In brief, granule unirefringence determines scattared energy and the ratio of scattared energy not, and granule repeatedly reflects decision scattering angle variance.Therefore, Beer law is equally followed in the decay of delustring attenuation and absorption.If the incident ray energy is 1, scattered beam does not continue to propagate along incident direction, its entrained energy, i.e. and delustring decays to exp (Γ (x, y)), and the scattered beam energy is 1-exp (Γ (x, y)).Under the condition of scattering center symmetry, sample a bit (x, y) can be expressed as the scattering by this light:

The following formula left side represents incident beam, and irradiating light beam is expressed on the right, wherein

Expression beam angle vector.(8) formula can also be written as weight expression:

In first on (8) formula or (9) formula the right

$\mathrm{\Γ}(x,y)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{\γ}(x,y,z)\mathrm{dz},---\left(10\right)$

Wherein γ (x, y, z) is the linear extinction coefficient of sample, σ in second ²(x, y) is the scattering angle variance that (x, y) some place sample integral thickness produces.Because the scattering angle variances sigma of sample integral thickness ²(x, y) is that a series of thickness are Δ z on the light transmition path _iThe scattering angular variance Δ σ of thin slice ²(x, y, z) sum, so the scattering angle variance of sample integral thickness can be expressed as:

${\mathrm{\σ}}^2(x,y)=\underset{{\mathrm{\Δz}}_i\→0}{\lim }\underset{i}{\mathrm{\Σ}}{\mathrm{\Δ\σ}}^2(x,y,z)$

$=\underset{{\mathrm{\Δz}}_i\→0}{\lim }\underset{i}{\mathrm{\Σ}}\mathrm{\ω}(x,y,z){\mathrm{\Δz}}_i=\underset{-\∞}{\overset{+\∞}{\∫}}\mathrm{\ω}(x,y,z){\mathrm{dz}}^{,---\left(11\right)}$

Wherein ω (x, y, z) is the linear scattering coefficient.In order to set up the relation between linear scattering coefficient and the linear extinction coefficient, (11) formula and (10) formula are compared, can get:

ω(x,y,z)＝ε(x,y,z)γ(x,y,z)， (12)

Wherein ε (x, y, z) is invasin.If sample is when being made of the identical material of scattering nature, invasin ε (x, y, z) is exactly constant, and then following formula is set up:

σ(x,y)＝ε·Γ(x,y)。(13)

This moment just can be from the another kind of signal of a kind of signal acquisition.In other words, if sample is when being made of the identical material of scattering nature, then two different scattered signals of geometric meaning can be summed up as a signal.

Consider above-mentioned three kinds of effects, under the centrosymmetric condition of sample scattering, a bit (x, y) can use the thing function to the effect by this light in the sample

Express,

Its weight expression is:

According to (15) formula, the thing function that only works at directions X as can be known is:

； (16)

The thing function that only works in Y-direction is:

。(17)

According to (14) formula or (15) formula, the outgoing X ray has carried following four kinds of sample signals as can be known:

(1) attenuation by absorption exp (Μ (x, y)), wherein Μ (x, y) is the projection path integration of linear absorption coefficient μ (x, y, z) $M(x,y)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{\μ}(x,y,z)\mathrm{dz};$

(2) refraction angle $\stackrel{\→}{\mathrm{\θ}}(x,y)={\stackrel{\→}{e}}_x{\mathrm{\θ}}_x(x,y)+{\stackrel{\→}{e}}_y{\mathrm{\θ}}_y(x,y),$ Wherein

Be the unit vector of directions X,

Be the unit vector of Y-direction, θ _x(x, y) is the projection path integration of the partial derivative of sample refractive index real part attenuation rate δ (x, y, z) directions X

θ _y(x, y) is the projection path integration of the partial derivative of sample refractive index real part attenuation rate δ (x, y, z) Y-direction

(3) delustring decay exp (Γ (x, y)), wherein Γ (x, y) is the projection path integration of linear extinction coefficient γ (x, y, z) $\mathrm{\Γ}(x,y)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{\γ}(x,y,z)\mathrm{dz};$

(4) scattering angle variances sigma ²(x, y) is the projection path integration of linear scattering coefficient:

${\mathrm{\σ}}^2(x,y)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{\ω}(x,y,z)\mathrm{dz},$

Pass between linear scattering coefficient and the linear extinction coefficient is:

ω(x,y,z)＝ε(x,y,z)γ(x,y,z)，

Wherein ε (x, y, z) is invasin.If sample is to be made of the identical material of scattering nature, invasin ε is constant just, and then the pass between linear scattering coefficient and the linear extinction coefficient is:

ω(x,y,z)＝ε·γ(x,y,z)，

Pass between delustring decay and the scattering angle variance is:

σ ²(x,y)＝ε·Γ(x,y)。

The 3rd step: set up the grating shearing imaging equation.

When before or after sample is put into beam-splitting optical grating, sample produces absorption, refraction and scattering process to the one dimension beam array that described beam-splitting optical grating produces, and analyzes the one dimension beam array that grating pair loaded sample message and carries out filtering.Because beam-splitting optical grating and acting on the imaging surface of analysis grating pair incident beam are translation invariant, when being n.s., the displacement curve that each resolution element records is identical, so detector is the convolution of thing function and displacement curve in the light distribution that the analysis grating records later.The grating shearing imaging equation can be from the thing function O of X or Y direction effect _{X, y}(x, y, θ _g) and displacement curve S (θ _g) convolution derive and go out:

$I(x,y,{\mathrm{\θ}}_g)=I_0{\mathrm{\θ}}_{x,y}(x,y,{\mathrm{\θ}}_g)*S\left({\mathrm{\θ}}_g\right)$

$=I_0\exp (-M(x,y)).$

$\{\exp (-\mathrm{\Γ}(x,y))\mathrm{\δ}({\mathrm{\θ}}_g-{\mathrm{\θ}}_{x,y}(x,y))+[1-\exp (-\mathrm{\Γ}(x,y))\left]\frac{\exp \left[\frac{{({\mathrm{\θ}}_g-{\mathrm{\θ}}_{x,y}(x,y))}^2}{{2\mathrm{\σ}}^2(x,y)}\right]}{\sqrt{2\mathrm{\π}}\mathrm{\σ}(x,y)}\right\},---\left(18\right)$

$*\stackrel{\‾}{S}[1+V_0\cos \left(\frac{2\mathrm{\πD}}{p}{\mathrm{\θ}}_g\right)]$

$=I_0\stackrel{\‾}{S}\exp (-M(x,y))[1+V(x,y)\cos \left(\frac{2\mathrm{\πD}}{p}({\mathrm{\θ}}_g-{\mathrm{\θ}}_{x,y}(x,y))\right)]$

Wherein, I ₀The incident light light intensity of beam-splitting optical grating during for n.s., exp (Μ (x, y)) is the attenuation by absorption picture, θ _{X, y}(x, y) is refraction angle picture, wherein θ _gBe to analyze the relative beam-splitting optical grating of grating along the angle of shear displacement of X or Y direction, V (x, y) is called again the visibility picture of sample for putting into the visibility of displacement curve behind the sample, and its expression formula is:

$V(x,y)=V_0.$

$\{\exp (-\mathrm{\Γ}(x,y))+\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\πD}}{p}\mathrm{\σ}(x,y)\right)}^2]-\exp [-\mathrm{\Γ}(x,y)-\frac{1}{2}{\left(\frac{2\mathrm{\πD}}{p}\mathrm{\σ}(x,y)\right)}^2\left]\right\}.---\left(19\right)$

The visibility of displacement curve during for n.s., exp (Γ (x, y)) is the delustring decay picture of sample, σ ²(x, y) is the scattering angle variance picture of sample.

In the step (f2), the process of described " try to achieve the mathematic(al) representation of the projection image that detector gathers: the mathematic(al) representation of trying to achieve respectively described light field image, dark field image and half light field image according to described grating shearing imaging equation " is:

If the shear displacemant x of the one dimension beam array that the relatively described beam-splitting optical grating of described analysis grating produces _gOr y _gBe respectively:

x _g=0 or y _g=0,

The shearing angular displacement of the relatively described beam-splitting optical grating of described analysis grating _gFor:

${\mathrm{\θ}}_g=\frac{x_g}{D}=0$ Or ${\mathrm{\θ}}_g=\frac{y_g}{D}=0,$

The one dimension beam array that namely in experiment described beam-splitting optical grating is produced and the shear displacemant between the described analysis grating are fixed on the bright field position, and background is bright field, puts into the light field image I that sample photodetector can collect sample _Bright(x, y), according to (18) formula, its expression formula is:

$I_{\mathrm{Bright}}(x,y)=I_0\stackrel{\‾}{S}\exp (-M(x,y))[1+V(x,y)\cos \left(\frac{2\mathrm{\πD}}{p}{\mathrm{\θ}}_{x,y}(x,y)\right)];---\left(20\right)$

If the shear displacemant x of the one dimension beam array that the relatively described beam-splitting optical grating of described analysis grating produces _gOr y _gBe respectively:

$x_g=\&PlusMinus;\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2}$ Or $y_g=\&PlusMinus;\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2},$

The shearing angular displacement of the relatively described beam-splitting optical grating of described analysis grating _gFor:

${\mathrm{\&theta;}}_g=\frac{x_g}{D}=\&PlusMinus;\frac{p}{2D}$ Or ${\mathrm{\&theta;}}_g=\frac{y_g}{D}=\&PlusMinus;\frac{p}{2D},$

The one dimension beam array that namely in experiment beam-splitting optical grating is produced and the shear displacemant of analyzing between the grating are fixed on the details in a play not acted out on stage, but told through dialogues position, and background is details in a play not acted out on stage, but told through dialogues, puts into sample photodetector and can collect dark field image I _Dark(x, y), according to (18) formula, its expression formula is:

$I_{\mathrm{Dark}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\cos \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_{x,y}(x,y)\right)];---\left(21\right)$

If the shear displacemant x of the one dimension beam array that the relatively described beam-splitting optical grating of described analysis grating produces _gOr y _gBe respectively:

$x_g=\frac{\mathrm{<figure-callout\; id="4"\; label="p"\; filenames="HDA00002998468900031.png"\; state="\{\{state\}\}">p</figure-callout>}}{4}$ Or $y_g=\frac{\mathrm{<figure-callout\; id="4"\; label="p"\; filenames="HDA00002998468900031.png"\; state="\{\{state\}\}">p</figure-callout>}}{4},$

Analyze the shearing angular displacement of the relatively described beam-splitting optical grating of grating _gFor:

${\mathrm{\&theta;}}_g=\frac{x_g}{D}=\frac{p}{4D}$ Or ${\mathrm{\&theta;}}_g=\frac{y_g}{D}=\frac{p}{4D},$

The one dimension beam array and the shear displacemant between the described analysis grating that namely in experiment described beam-splitting optical grating are produced are fixed on right half bright field or first bright field position, background is right half bright field or first bright field, put into sample, according to (18) formula, the right side half light field image I that detector collects _Right(x, y) expression formula is:

$I_{\mathrm{Right}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1+V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)];---\left(22\right)$

First light field image I _Up(x, y) expression formula is:

$I_{\mathrm{Up}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1+V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)];---\left(23\right)$

If the shear displacemant x of the one dimension beam array that the relatively described beam-splitting optical grating of described analysis grating produces _gOr y _gBe respectively:

$x_g=-\frac{\mathrm{<figure-callout\; id="4"\; label="p"\; filenames="HDA00002998468900031.png"\; state="\{\{state\}\}">p</figure-callout>}}{4}$ Or $y_g=-\frac{\mathrm{<figure-callout\; id="4"\; label="p"\; filenames="HDA00002998468900031.png"\; state="\{\{state\}\}">p</figure-callout>}}{4},$

The shearing angular displacement of the relatively described beam-splitting optical grating of described analysis grating _gFor:

${\mathrm{\&theta;}}_g=\frac{x_g}{D}=-\frac{p}{4D}$ Or ${\mathrm{\&theta;}}_g=\frac{y_g}{D}=-\frac{p}{4D},$

The one dimension beam array and the shear displacemant between the described analysis grating that namely in experiment described beam-splitting optical grating are produced are fixed on left half bright field or second bright field position, background is left half bright field or second bright field, put into sample, according to (18) formula, a left side half light field image I that detector collects _Left(x, y) expression formula is:

$I_{\mathrm{Left}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)];---\left(24\right)$

Second light field image I _Down(x, y) expression formula is:

$I_{\mathrm{Down}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)].---\left(25\right)$

In the step (f3), the process of described " respectively the mathematic(al) representation of described light field image, dark field image and half light field image is out of shape, obtains the semi-quantitative expressed formula of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample " is:

Under the condition of ignoring sample refraction and scattering,

θ _x，y(x，y)≈0，V(x，y)≈V ₀，

According to (20) formula or (21) formula, the semi-quantitative expressed formula of attenuation by absorption picture is:

$\exp (-M(x,y))=\frac{I_{\mathrm{Bright}}(x,y)}{(1+V_0)I_0\stackrel{\&OverBar;}{S}},---\left(26\right)$

Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Dark}}(x,y)}{I_0(1-V_0)\stackrel{\&OverBar;}{S}};---\left(27\right)$ Under the condition of ignoring absorption of sample and scattering,

M(x，y)≈0，V(x，y)≈V ₀，

When described each grating grizzly bar direction is parallel to the sample rotating shaft, according to (22) formula or (24) formula, perpendicular to the semi-quantitative expressed formula of the refraction angle picture of sample rotating shaft be:

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_{\mathrm{Right}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right),---\left(28\right)$

Or,

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Left}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right),---\left(29\right)$

During in the sample rotating shaft, according to (23) formula or (25) formula, the semi-quantitative expressed formula that is parallel to the refraction angle picture of sample rotating shaft is at described each grating grizzly bar perpendicular direction:

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_{\mathrm{Up}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right),---\left(30\right)$

Or,

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Down}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right);---\left(31\right)$

Under the condition of ignoring absorption of sample and refraction,

M(x，y)≈0，θ _x，y(x，y)≈0，

According to (20) formula or (21) formula, the semi-quantitative expressed formula of described visibility picture is:

$V(x,y)=\frac{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}},---\left(32\right)$

Or

$V(x,y)=\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Dark}}(x,y)}{I_0\stackrel{\&OverBar;}{S}};---\left(33\right)$

Under the weak scattering condition,

$0\&le;\mathrm{\&sigma;}(x,y)<<\frac{p}{D}\&DoubleRightArrow;0\&le;\frac{D}{p}\mathrm{\&sigma;}(x,y)<<1,$

Have:

$\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2]>>\{1-\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2\left]\right\}$ ， (34)

$>\exp (-\mathrm{\&Gamma;}(x,y))\{1-\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2\left]\right\}$

(34) formula substitution (19) formula,

$V(x,y)\&ap;V_0\exp \left[{-\frac{1}{2}\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2\right],---\left(35\right)$

(32) formula or (33) formula substitution (35) formula, the semi-quantitative expressed formula that gets scattering angle variance picture is:

${\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{V(x,y)}=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}};---\left(36\right)$

Or

${\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{V(x,y)}=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}-I_{\mathrm{Dark}}(x,y)};---\left(37\right)$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the semi-quantitative expressed formula of described linear delustring picture is:

$\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))=\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}],---\left(38\right)$

Or

$\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))=\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Dark}}(x,y)}];---\left(39\right)$

Under the strong scattering condition, $\mathrm{\&sigma;}(x,y)\&GreaterEqual;\frac{p}{D},$

Have:

$\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2]\&le;\exp \left({-2\mathrm{\&pi;}}^2\right)\&ap;0,---\left(40\right)$

Have:

$\exp (-\mathrm{\&Gamma;}(x,y))>>[1-\exp (-\mathrm{\&Gamma;}(x,y))]$

$>\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2][1-\exp (-\mathrm{\&Gamma;}(x,y)){]}^{,---\left(41\right)}$

(41) formula substitution (19) formula:

V(x，y)≈V ₀exp(-Γ(x，y))， (42)

(32) formula or (33) formula substitution (42) formula, the semi-quantitative expressed formula that gets delustring decay picture is:

$\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}=\frac{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}};---\left(43\right)$

Or

$\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}=\frac{I_0\stackrel{\&OverBar;}{S}-I_{\mathrm{Dark}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}};---\left(44\right)$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and described scattering angle variance picture fixed partly measured expression formula and be:

${\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{V(x,y)}=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}},---\left(45\right)$

Or

${\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{V(x,y)}=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{{I_0\stackrel{\&OverBar;}{S}-I}_{\mathrm{Dark}}(x,y)}.---\left(46\right)$

In the step (f4), the process of described " according to the quantitative relationship between the mathematic(al) representation of described light field image, dark field image and half light field image, obtaining the quantitative expression of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample " is as follows:

According to (20) formula and (21) formula, or (22) formula and (24) formula, or (23) formula with the quantitative expression that (25) formula gets the attenuation by absorption picture is:

$\exp (-M(x,y))=\frac{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}},---\left(47\right)$

Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}},---\left(48\right)$

Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}},---\left(49\right)$

Described light field image, dark field image, right half light field image/first light field image and left half light field image/second light field image are aimed at one by one according to respective pixel, and carried out additive operation according to described formula;

When described each grating grizzly bar direction was parallel to the sample rotating shaft, according to (20) formula, (21) formula, (22) formula and (24) formula, described refraction angle perpendicular to the sample rotating shaft can obtain from following system of equations as quantitative expression:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_x(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arctan \left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}\right)\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,---\left(50\right)$

During in the sample rotating shaft, according to (20) formula, (21) formula, (23) formula and (25) formula, the described refraction angle that is parallel to the sample rotating shaft can obtain from following system of equations as quantitative expression at described each grating grizzly bar perpendicular direction:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_y(x,y)=\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)\arctan \left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}\right)\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array};\right.---\left(51\right)$

Light field image, dark field image, right half light field image/first light field image and left half light field image/second light field image are aimed at one by one according to respective pixel, and carried out subtraction, division and arctangent cp cp operation according to described formula;

Under the weak scattering condition, according to (34) formula, (20) formula, (21) formula, (22) formula and (24) formula or (23) formula and (25) formula, the quantitative expression of described scattering angle variance picture can obtain from following system of equations:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,---\left(52\right)$

Or,

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;---\left(53\right)$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the quantitative expression of described delustring decay picture can obtain from following system of equations:

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))\\ =\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}]\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,---\left(55\right)$

Or,

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))\\ =\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002998468900012.png"\; state="\{\{state\}\}">p</figure-callout>}}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}]\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;---\left(56\right)$

Light field image, dark field image, right half light field image/first light field image and left half light field image/second light field image are aimed at one by one according to respective pixel, and carried out addition, subtraction, division, power, evolution and logarithm operation according to described formula;

Under the strong scattering condition, according to (41) formula, (20) formula, (21) formula, (22) formula and (24) formula or (23) formula and (25) formula, the quantitative expression of described delustring decay picture can obtain from following system of equations:

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}\\ =\frac{1}{V_0}\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,---\left(57\right)$

Or,

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}\\ =\frac{1}{V_0}\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;---\left(58\right)$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the quantitative expression of described scattering angle variance picture can obtain from following system of equations:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)\\ =\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,---\left(59\right)$

Or,

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)\\ =\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right..---\left(60\right)$

Light field image, dark field image, right half light field image/first light field image and left half light field image/second light field image are aimed at one by one according to respective pixel, and carried out addition, subtraction, division, power, evolution and logarithm operation according to described formula.

Claims (16)

1. a grating shearing two-dimensional imaging system is characterized in that, comprising:

Light supply apparatus, for generation of many seam light sources, every seam light source all produces the X ray light beam of illumination beam splitter grating;

Beam-splitting optical grating, being used for described light beam beam splitting is the One Dimension Periodic beam array;

Sample stage is used for the carrying sample;

Analyze grating, for generation of different light intensity backgrounds, refraction signal or the scattered signal of enhancer or inhibitor sample;

Detector is used for surveying the background of light intensity and the variation of locus, gathers the projection image of described sample under the different light intensity background.

2. grating shearing two-dimensional imaging according to claim 1 system, it is characterized in that, described light supply apparatus comprises pointolite or seam light source, or described light supply apparatus comprises expansion light source and light source grating, or described light supply apparatus is the grizzly bar target with light source grating complementary structure; Described light source grating is used for that described expansion light source is divided into one dimension and stitches light source more, or described grizzly bar target directly produces one dimension and stitches light source more.

3. grating shearing two-dimensional imaging according to claim 1 system is characterized in that, described sample stage is arranged between beam-splitting optical grating and the light supply apparatus and the setting of next-door neighbour's beam-splitting optical grating; Or described sample stage is arranged at beam-splitting optical grating and analyzes between the grating and the setting of next-door neighbour's beam-splitting optical grating.

4. grating shearing two-dimensional imaging according to claim 2 system is characterized in that,

Described light source grating is pressed close to described light source and is placed; The grizzly bar of described light source grating be wider than or equal to stitch wide, or the grizzly bar of described grizzly bar target be less than or equal to the seam wide;

Described light source grating, described beam-splitting optical grating and described analysis grating are absorption grating or described beam-splitting optical grating is phase grating, and described light source grating and described analysis grating are absorption grating; And/or,

The period-producer pin-hole imaging relation of the cycle of described light source grating or described grizzly bar target and described analysis grating, pin hole is any seam on the beam-splitting optical grating; And/or,

Described beam-splitting optical grating and the distance of analyzing between the grating are 0.1～5 meter; And/or,

The cycle of described beam-splitting optical grating is 1～100 micron; And/or,

The grizzly bar of described beam-splitting optical grating is wide and seam is wide equates; And/or,

The cycle of described analysis grating equals 1/2nd of the geometric projection in described beam-splitting optical grating cycle or geometric projection; And/or,

The grizzly bar of described analysis grating is wide and seam is wide equates; And/or,

Described detector is pressed close to described analysis grating and is placed; And/or,

Described detector comprises one dimensional linear array or the two-dimensional array that a plurality of probe units consist of,

Described grizzly bar target is the structure of setting that target light source and light source grating are become one.

5. grating shearing two-dimensional imaging according to claim 2 system, it is characterized in that, when described light source grating or beam-splitting optical grating or described analysis grating were absorption grating, its grizzly bar thickness was for making at least through light intensity attenuation to 10% of incident intensity required thickness; When described beam-splitting optical grating was phase grating, its grizzly bar thickness needed to make the phase shift that obtains π or pi/2 through light beam.

6. a grating shearing two-dimensional imaging method is characterized in that, comprising:

Adjust light supply apparatus, the light beam irradiates beam-splitting optical grating that described light supply apparatus is produced;

Adjust beam-splitting optical grating, make the beam-splitting optical grating plane perpendicular to the described beam center direction of propagation, and be the One Dimension Periodic beam array with described light beam beam splitting;

Adjust and analyze grating, the one dimension beam array that the described beam-splitting optical grating of described analysis grating alignment is produced;

Measure displacement curve: when n.s., survey the variation of background light intensity by detector, in the plane of the normal beam direction of propagation, move described light source grating or grizzly bar target or beam-splitting optical grating or analyze grating along the direction perpendicular to grizzly bar, adjust the shear displacemant between the one dimension beam array of analyzing grating and beam-splitting optical grating generation, detector records the displacement curve that background light intensity shear displacemant changes;

The projection image of detector collected specimens: the shear displacemant between the one dimension beam array of analyzing the generation of grating and described beam-splitting optical grating is adjusted at the collection position that the background light intensity satisfies imaging requirements, put into sample, gather the projection image of described sample under the different light intensity background by described detector.

7. grating shearing two-dimensional imaging method according to claim 6, it is characterized in that, described light supply apparatus comprises expansion light source and light source grating, or described light supply apparatus is the grizzly bar target with light source grating complementary structure, described " adjusting light supply apparatus; the light beam irradiates beam-splitting optical grating that described light supply apparatus is produced " is specially " adjust light source and light source grating; make light source grating that described light source is divided into one dimension and stitch light source more; or adjust the one dimension that the grizzly bar target produces and stitch light source more, make every seam light source can both produce the light beam irradiates beam-splitting optical grating ".

8. grating shearing two-dimensional imaging method according to claim 6 is characterized in that,

Described light intensity background comprises: bright field background, details in a play not acted out on stage, but told through dialogues background and/or half bright field background; Described half bright field background comprises right half bright field background and/or left half bright field background, perhaps comprises first bright field background and/or second bright field background;

Described acquired projections looks like to comprise: gather described sample at the light field image under the described bright field background, at the dark field image under the described details in a play not acted out on stage, but told through dialogues background and/or half light field image under described half bright field background; Described half light field image comprises: left half light field image and/or right half light field image perhaps comprise first light field image and/or second light field image.

9. each described grating shearing two-dimensional imaging method is characterized in that according to claim 6-8, also comprises the sxemiquantitative of the described sample of extraction from the projection image of described collection or the step of quantitative description information after the projection image of detector collected specimens.

10. grating shearing two-dimensional imaging method according to claim 9 is characterized in that, sxemiquantitative or the quantitative description information of extracting described sample from the projection image of described collection specifically comprise:

Set up the grating shearing imaging equation: with the displacement curve that the cosine function curve records, set up thing function mathematical model, according to the convolution algorithm of thing function and match displacement curve, set up the grating shearing imaging equation;

Try to achieve the mathematic(al) representation of the projection image of detector collection: the mathematic(al) representation of trying to achieve respectively described light field image, dark field image and half light field image according to described grating shearing imaging equation;

Respectively the mathematic(al) representation of described light field image, dark field image and half light field image is out of shape, tries to achieve the semi-quantitative expressed formula of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample;

Or,

According to the quantitative relationship between the mathematic(al) representation of described light field image, dark field image and half light field image, obtain the quantitative expression of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample.

11. grating shearing two-dimensional imaging method according to claim 10 is characterized in that, describedly sets up the match displacement curve S (θ described in the grating shearing imaging equation step _g) Mathematical representation be:

$S\left({\mathrm{\&theta;}}_g\right)\&ap;\stackrel{\&OverBar;}{S}[1+V_0\cos \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_g\right)];$

S (θ wherein _g) ratio of incident intensity before the beam-splitting optical grating when light intensity surveyed for detector and n.s., D is beam-splitting optical grating and analyzes distance between the grating, p is for analyzing the cycle of grating and displacement curve,

Displacement curve mean value during for n.s., The visibility of displacement curve during for n.s., S _MaxAnd S _MinBe respectively maximal value and the minimum value of displacement curve, θ _gFor analyzing the relative beam-splitting optical grating of grating edge perpendicular to the angle of shear displacement of the direction of grizzly bar, when the grizzly bar direction is parallel to the sample rotating shaft,

x _gFor analyzing one dimension beam array that the relative beam-splitting optical grating of grating produces along the shear displacemant perpendicular to the direction of grizzly bar, when grizzly bar perpendicular direction during in the sample rotating shaft, y _gFor analyzing one dimension beam array that the relative beam-splitting optical grating of grating produces along the shear displacemant perpendicular to the direction of grizzly bar.

12. grating shearing two-dimensional imaging method according to claim 10 is characterized in that, described thing function

To the effect by this light, expression formula is to express in the sample a bit (x, y):

Or,

Wherein only at the thing function of x directive effect be:

Only the thing function in the y directive effect is:

Wherein,

Express irradiating light beam angle vector, With

Be respectively

Component along directions X and Y-direction;

In the thing function, the mathematical expression of attenuation by absorption picture is:

exp(-Μ(x,y))，

Wherein Μ (x, y) is the projection path integration of linear absorption coefficient μ (x, y, z):

$M(x,y)=\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\mathrm{\&mu;}(x,y,z)\mathrm{dz};$

The mathematical expression of refraction angle picture is:

$\stackrel{\&RightArrow;}{\mathrm{\&theta;}}(x,y)={\stackrel{\&RightArrow;}{e}}_x{\mathrm{\&theta;}}_x(x,y)+{\stackrel{\&RightArrow;}{e}}_y{\mathrm{\&theta;}}_y(x,y),$

Wherein

Be the unit vector of directions X, Be the unit vector of Y-direction, θ _x(x, y) be sample along the refraction angle of directions X, also be refractive index real part attenuation rate δ (x, y, z) along the projection path integration of directions X partial derivative:

${\mathrm{\&theta;}}_x(x,y)=-\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\frac{\&PartialD;\mathrm{\&delta;}(x,y,z)}{\&PartialD;x}\mathrm{dz},$

θ _y(x, y) be sample along the refraction angle of Y-direction, also be sample refractive index real part attenuation rate δ (x, y, z) along the projection path integration of Y-direction partial derivative:

${\mathrm{\&theta;}}_y(x,y)=-\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\frac{\&PartialD;\mathrm{\&delta;}(x,y,z)}{\&PartialD;y}\mathrm{dz};$

The mathematical expression of delustring decay picture is:

exp(-Γ(x,y))，

Wherein Γ (x, y) is the projection path integration of linear extinction coefficient γ (x, y, z):

$\mathrm{\&Gamma;}(x,y)=\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}\mathrm{\&gamma;}(x,y,z)\mathrm{dz};$

The mathematical expression of scattering angle variance is:

σ ²(x,y)，

It is each differential thin layer dz scattering angle variance d σ ²The projection path integration of (x, y, z):

${\mathrm{\&sigma;}}^2(x,y)=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}{\mathrm{d\&sigma;}}^2(x,y,z)=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}\mathrm{\&omega;}(x,y,z)\mathrm{dz},$

Wherein ω (x, y, z) is the linear scattering coefficient, and the pass between itself and the linear extinction coefficient is:

ω(x,y,z)＝ε(x,y,z)γ(x,y,z)，

Wherein ε (x, y, z) is invasin, if sample is made of the identical material of scattering nature, ε (x, y, z) is constant, and then following formula is set up:

σ ²(x,y)＝ε·Γ(x,y)。

13. grating shearing two-dimensional imaging method according to claim 10 is characterized in that: described grating image equation is:

$I(x,y,{\mathrm{\&theta;}}_g)=I_0{\mathrm{\&theta;}}_{x,y}(x,y,{\mathrm{\&theta;}}_g)*S\left({\mathrm{\&theta;}}_g\right)$

$=I_0\stackrel{\&OverBar;}{S}\exp (-M(x.y))[1+V(x,y)\cos \left(\frac{2\mathrm{\&pi;D}}{p}({\mathrm{\&theta;}}_g-{\mathrm{\&theta;}}_{x,y}(x,y))\right)];$

When the grizzly bar direction is parallel to the sample rotating shaft,

$O_{x,y}(x,y,{\mathrm{\&theta;}}_g)=O_x(x,y,{\mathrm{\&theta;}}_g),{\mathrm{\&theta;}}_{x,y}(x,y)={\mathrm{\&theta;}}_x(x,y),{\mathrm{\&theta;}}_g=\frac{x_g}{D};$

When grizzly bar perpendicular direction during in the sample rotating shaft,

$O_{x,y}(x,y,{\mathrm{\&theta;}}_g)=O_y(x,y,{\mathrm{\&theta;}}_g),{\mathrm{\&theta;}}_{x,y}(x,y)={\mathrm{\&theta;}}_y(x,y),{\mathrm{\&theta;}}_g=\frac{y_g}{D};$

Wherein D is the distance between beam-splitting optical grating and the analysis grating, and p is for analyzing the cycle of grating and displacement curve, I (x, y, θ _g) on the sample surveyed for detector a bit (x, y) be θ in angle of shear displacement _gThe time light intensity, I ₀Incident intensity before the beam-splitting optical grating during for n.s.,

Displacement curve mean value during for n.s., S _MaxAnd S _MinBe respectively maximal value and the minimum value of displacement curve, θ _x(x, y) is that sample is along the refraction angle of directions X, θ _y(x, y) be sample along the refraction angle of Y-direction, the visibility of V (x, y) displacement curve when sample is arranged claims again the visibility picture of sample, its expression formula is:

$V(x,y)$

$=V_0\{\exp (-\mathrm{\&Gamma;}(x,y))+\exp [-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2]-\exp [-\mathrm{\&Gamma;}(x,y)-\frac{1}{2}{\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2\left]\right\},$

The visibility of displacement curve during for n.s., exp (Γ (x, y)) is delustring decay picture, σ ²(x, y) is scattering angle variance picture.

14. grating shearing two-dimensional imaging method according to claim 13 is characterized in that, in described " trying to achieve the mathematic(al) representation of described acquired projections picture " step,

The angle of shear displacement of corresponding described bright field background

Or Described light field image I _BrightThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Bright}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x.y))[1+V(x,y)\cos \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_{x,y}(x,y)\right)];$

The angle of shear displacement of corresponding described details in a play not acted out on stage, but told through dialogues background

Or Described dark field image I _DarkThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Dark}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\cos \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_{x,y}(x,y)\right)];$

The angle of shear displacement of the corresponding described right side half bright field background

The described right side half light field image I _RightThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Right}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x.y))[1+V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)];$

The angle of shear displacement of a corresponding described left side half bright field background

A described left side half light field image I _LeftThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Left}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_x(x,y)\right)];$

The angle of shear displacement of corresponding described first bright field background

Described first light field image I _UpThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Up}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1+V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_y(x,y)\right)],$

The angle of shear displacement of corresponding described second bright field background

Second light field image I _DownThe mathematic(al) representation of (x, y) is:

$I_{\mathrm{Down}}(x,y)=I_0\stackrel{\&OverBar;}{S}\exp (-M(x,y))[1-V(x,y)\sin \left(\frac{2\mathrm{\&pi;D}}{p}{\mathrm{\&theta;}}_y(x,y)\right)].$

15. grating shearing two-dimensional imaging method according to claim 14, it is characterized in that, in described " respectively the mathematic(al) representation of described light field image, dark field image and half light field image being out of shape; obtain the semi-quantitative expressed formula of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample " step

Under the condition of ignoring sample refraction and scattering,

θ _x,y(x,y)≈0，V(x,y)≈V ₀，

The semi-quantitative expressed formula of described attenuation by absorption picture is:

$\exp (-M(x,y))=\frac{I_{\mathrm{Bright}}(x,y)}{(1+V_0)I_0\stackrel{\&OverBar;}{S}},$

Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Dark}}(x,y)}{I_0(1-V_0)\stackrel{\&OverBar;}{S}};$

Under the condition of ignoring absorption of sample and scattering,

Μ(x,y)≈0，V(x,y)≈V ₀，

When described each grating grizzly bar direction was parallel to the sample rotating shaft, the semi-quantitative expressed formula of described refraction angle picture perpendicular to the sample rotating shaft was:

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_{\mathrm{Right}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right),$

Or

${\mathrm{\&theta;}}_x(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Left}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right);$

During in the sample rotating shaft, the described semi-quantitative expressed formula that is parallel to the refraction angle picture of sample rotating shaft is at described each grating grizzly bar perpendicular direction:

${\mathrm{\&theta;}}_y(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_{\mathrm{Up}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right),$

Or

${\mathrm{\&theta;}}_y(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arcsin \left(\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Down}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}}\right);$

Under the condition of ignoring absorption of sample and refraction,

Μ(x,y)≈0，θ _x,y(x,y)≈0，

The semi-quantitative expressed formula of described visibility picture is:

$V(x,y)=\frac{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}},$

Or

$V(x,y)=\frac{I_0\stackrel{\&OverBar;}{S}{-I}_{\mathrm{Dark}}(x,y)}{I_0\stackrel{\&OverBar;}{S}};$

Under the weak scattering condition, the pass of scattering angle variance picture and visibility picture is:

$V(x,y)=V_0\exp \left[{-\frac{1}{2}\left(\frac{2\mathrm{\&pi;D}}{p}\mathrm{\&sigma;}(x,y)\right)}^2\right],$

The semi-quantitative expressed formula that gets scattering angle variance picture is:

${\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{V(x,y)}={\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \left(\frac{I_0{V}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}\right),$

Or

${\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{V(x,y)}={\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \left(\frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}{I}_{\mathrm{Dark}}(x,y)}\right);$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the semi-quantitative expressed formula of described delustring decay picture is:

$\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))=\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}],$

Or

$\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))=\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_0\stackrel{\&OverBar;}{S}-I_{\mathrm{Dark}}(x,y)}];$

Under the strong scattering condition,

V(x,y)＝V ₀exp[-Γ(x,y)]，

The semi-quantitative expressed formula that gets delustring decay picture is:

$\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}=\frac{I_{\mathrm{Bright}}(x,y)-I_0\stackrel{\&OverBar;}{S}}{V_0{I}_0\stackrel{\&OverBar;}{S}};$

Or

$\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}=\frac{I_0\stackrel{\&OverBar;}{S}-I_{\mathrm{Dark}}(x,y)}{V_0{I}_0\stackrel{\&OverBar;}{S}};$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and described scattering angle variance picture fixed partly measured expression formula and be:

${\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{V(x,y)}=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{I_{\mathrm{Bright}}(x,y)I_0\stackrel{\&OverBar;}{S}},$

Or

${\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{V(x,y)}=\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0{I}_0\stackrel{\&OverBar;}{S}}{{I_0\stackrel{\&OverBar;}{S}-I}_{\mathrm{Dark}}(x,y)}.$

16. grating shearing two-dimensional imaging method according to claim 14, it is characterized in that, in described " according to the quantitative relationship between the mathematic(al) representation of described light field image, dark field image and half light field image; obtain the quantitative expression of attenuation by absorption picture, refraction angle picture, scattering angle variance picture or the delustring decay picture of described sample " step

Quantitative expression according to described attenuation by absorption picture:

$\exp (-M(x,y))=\frac{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}},$ Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}},$ Or

$\exp (-M(x,y))=\frac{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}{2I_0\stackrel{\&OverBar;}{S}};$

When described each grating grizzly bar direction was parallel to the sample rotating shaft, the quantitative expression of described refraction angle picture perpendicular to the sample rotating shaft obtained from following system of equations:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_x(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arctan \left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}\right)\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,$

During in the sample rotating shaft, the described quantitative expression that is parallel to the refraction angle picture of sample rotating shaft obtains from following system of equations at described each grating grizzly bar perpendicular direction:

$\left\{\begin{array}{c}{\mathrm{\&theta;}}_y(x,y)=\left(\frac{p}{2\mathrm{\&pi;D}}\right)\arctan \left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Down}}(x,y)}\right)\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;$

Under the weak scattering condition, obtain from following system of equations according to the quantitative expression of described scattering angle variance picture:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,$

Or

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=2{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the quantitative expression of described delustring decay picture obtains from following system of equations:

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))\\ =\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}]\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,$ Or

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\exp (-\frac{1}{\mathrm{\&epsiv;}}{\mathrm{\&sigma;}}^2(x,y))\\ =\exp [-\frac{2}{\mathrm{\&epsiv;}}{\left(\frac{p}{2\mathrm{\&pi;D}}\right)}^2\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}]\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;$

Under the strong scattering condition, the quantitative expression of described delustring decay picture obtains from following system of equations:

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}\\ =\frac{1}{V_0}\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,$

Or

$\left\{\begin{array}{c}\exp (-\mathrm{\&Gamma;}(x,y))=\frac{V(x,y)}{V_0}\\ =\frac{1}{V_0}\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.,$

At this moment, if sample is to be made of the identical material of scattering nature, then invasin ε is constant, and the quantitative expression of described scattering angle variance picture obtains from following system of equations:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)\\ =\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Right}}(x,y)-I_{\mathrm{Left}}(x,y)}{I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Right}}(x,y)+I_{\mathrm{Left}}(x,y)\end{array}\right.,$

Or

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}^2(x,y)=\mathrm{\&epsiv;}\&CenterDot;\mathrm{\&Gamma;}(x,y)\\ =\mathrm{\&epsiv;}\&CenterDot;\ln \frac{V_0}{\sqrt{{\left(\frac{I_{\mathrm{Bright}}(x,y)-I_{\mathrm{Dark}}(x,y)}{I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)}\right)}^2+{\left(\frac{I_{\mathrm{Up}}(x,y)-I_{\mathrm{Down}}(x,y)}{I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)}\right)}^2}}\\ I_{\mathrm{Bright}}(x,y)+I_{\mathrm{Dark}}(x,y)=I_{\mathrm{Up}}(x,y)+I_{\mathrm{Down}}(x,y)\end{array}\right.;$

With unidirectional light field image, dark field image, right half light field image/first light field image and left half light field image/second light field image, aim at one by one according to respective pixel, and carry out addition, subtraction, division, power, evolution and logarithm operation according to described formula.

Images